Reducing harmonic distortion by dithering
A digital signal generation assumes that a base frequency (the frequency with which the primitive phase angles are specified relative to) is equal to the carrier frequency for all relevant times. But this causes errors in the digital signals output to each array element transducer. Thus, it is necessary for the development of a signal generation system that is capable of producing a digital signal using the free selection of amplitude and phase. This is used to produce a substantially error-free signal that preserves the amplitude and phase relative to a constant base frequency while allowing the carrier frequency to vary.
1. A system comprising:
an electrical signal wherein the electrical signal is driven by a real-time progressive polynomial spline evaluation of interpolated phase angle samples that achieves an up-sampling by a power-of-two factor using a linear combination;
wherein a result of at least one of the spline evaluation is used to control an aspect of an output electrical signal;
wherein a resulting value of the spline evaluation when added to a base frequency phase counter is used to determine a location of an output signal edge of the output digital signal;
wherein the location is perturbed by a random dither on the phase angle drawn from a uniform distribution;
wherein action of the phase dither is variable in a time domain as a conversion from phase to an output time series is naturally dependent on instantaneous frequency of the location.
2. The system of claim 1 , wherein the polynomial spline has a plurality of intervals, and wherein at least one of the plurality of intervals is a base frequency period.
3. The system of claim 1 , wherein the polynomial spline has a plurality of intervals, and wherein at least one of the plurality of intervals is a power-of-two count of base frequency periods.
4. The system of claim 1 , wherein the polynomial spline has a plurality of intervals, and wherein at least one of the plurality of intervals is a power-of-two fraction of a base frequency period.
5. The system of claim 1 , wherein the electrical signal has a phase angle, and wherein the phase angle is modified by a rolling counter incremented by a value driven by an external environmental monitoring sensor.
6. The system of claim 1 , wherein the electrical signal has a phase angle, and wherein the phase angle is modified by a rolling counter decremented by a value driven by an external environmental monitoring sensor.
7. A system comprising:
an electrical signal wherein an instantaneous phase angle of the electrical signal is substantially calculated by a real-time progressive polynomial spline evaluation that achieves an up-sampling by a power-of-two factor using a linear combination of counters;
wherein a result of at least one of the spline evaluation is used to control an aspect of an output electrical signal;
wherein an interpolated phase angle added to a base frequency phase counter used to determine the location of an output signal edge of the output electrical signal,
has a further test applied to determine an update time free of possible race conditions to reinitialize random dither for its corresponding signal edge of the output digital signal.
8. The system of claim 7 , wherein the polynomial spline has a plurality of intervals, and wherein at least one of the plurality of intervals is a base frequency period.
9. The system of claim 7 , wherein the polynomial spline has a plurality of intervals, and wherein at least one of the plurality of intervals is a power-of-two count of base frequency periods.
10. The system of claim 7 , wherein the polynomial spline has a plurality of intervals, and wherein at least one of the plurality of intervals is a power-of-two fraction of a base frequency period.
11. The system of claim 7 , wherein the electrical signal has a phase angle, and wherein the phase angle is modified by a rolling counter incremented by a value driven by an external environmental monitoring sensor.
12. The system of claim 7 , wherein the electrical signal has a phase angle, and wherein the phase angle is modified by a rolling counter decremented by a value driven by an external environmental monitoring sensor.
13. The system of claim 7 , wherein the further applied test uses a contiguous subset of the binary digits of the resulting value of the spline evaluation of the interpolated phase angle samples when added to the base frequency phase counter to determine a race-condition free time.
14. The system of claim 13 , further comprising a polynomial spline having a plurality of intervals, and wherein at least one of the plurality of intervals is a base frequency period.
15. The system of claim 13 , further comprising a polynomial spline having a plurality of intervals, and wherein at least one of the plurality of intervals is a power-of-two count of base frequency periods.
16. The system of claim 13 , further comprising a polynomial spline having a plurality of intervals, and wherein at least one of the plurality of intervals is a power-of-two fraction of a base frequency period.
17. The system of claim 13 , wherein the electrical signal has a phase angle, and wherein the phase angle is modified by a rolling counter incremented by a value driven by an external environmental monitoring sensor.
18. The system of claim 13 , wherein the electrical signal has a phase angle, and wherein the phase angle is modified by a rolling counter decremented by a value driven by an external environmental monitoring sensor.
19. The system of claim 13 , further comprising;
using a Boolean result of the test to clock a linear feedback shift register (LFSR) to supply a new random value for the phase angle dither of its corresponding signal edge of the output digital signal.